Online Prediction Method for Reentry Footprint Based on Multi-Head Attention Neural Network

Abstract

The online prediction of reentry footprints is critical for autonomous systems in scenarios like emergency landing and mission replanning, yet it remains challenging to balance computational speed with predictive accuracy. This work presents a fast and accurate online prediction method based on a Multi-Head Attention Neural Network (MHANN) to overcome the limitations of traditional numerical and analytical approaches. The proposed model is trained on high-fidelity samples generated offline using the Gauss Pseudospectral Method (GPM). To handle the periodicity of longitude, we introduce a state expansion technique that represents longitude as continuous sine and cosine features, effectively eliminating numerical discontinuities. The network employs a lightweight Multi-Head Attention mechanism to capture complex dependencies between flight states and footprint boundaries efficiently. Furthermore, a custom loss function incorporating a trigonometric identity constraint is designed to ensure the physical consistency of predictions. Simulation results demonstrate the model’s superiority, achieving a training loss at least one order of magnitude lower than control groups. With only 86,969 parameters, the MHANN accomplishes an average inference time of 0.221ms on a platform with an Intel Core i9-14900HX CPU, reducing the prediction error by up to 88.6% compared to benchmarks. The combined use of state expansion and the physics-informed loss function is shown to be crucial, contributing to a dramatic 94% error reduction in ablation studies. This study confirms that the MHANN-based method delivers millisecond-level, high-accuracy footprint prediction, fulfilling the stringent real-time requirements of autonomous onboard systems.